Annie Oakley (Phoebe Ann ?)

On the Darke County, Ohio genealogy site found an obit for Annie's brother John.
http://genealogytrails.com/ohio/darke/obits.html
John H. Moses
Brother of Famed Annie Oakley Dies
John H. Moses, 86, brother of the world-famous woman marksman, Annie Oakley, die last Thursday at his home in Greenville. He and Mrs. Moses celebrated their 65th wedding anniversary on Feb. 27. Mr. Moses had six sisters, all whom preceded him in death. Annie, born at Willow Dell, north of Versailles, gained such great fame as a marksman that at one time her name was said to be familiar to more people the world over than that of any other woman. She died in 1926. Funeral services for Mr. Moses were held Sunday at Greenville and he was buried in Brock cemetery north of Greenville, beside Annie's grave. [Eaton Register, c. 1949]

Another website shows the family name as Moses but they couldn't agree on the correct spelling than either.
https://www.annieoakleycenterfoundation.com/faq.html
What was Annie's real name?

Portrait of a young Annie OakleyAnnie was christened Phoebe Ann, born on August 13, 1860, the fifth daughter of a poor Darke County, Ohio farm couple, Susan and Jacob Moses.

The family name has been ever since a source of confusion. Annie's brother, John, born a two years later,insisted that their name was Moses. Annie was equally insistent that it was Mosey, or Mozee. The family name had also apparently appeared in the census as Mauzy, and Jacob was buried as Mosey. For convenience, biographers have generally remembered her as Mrs. Annie Oakley Butler, née Phoebe Ann Moses.

Link to her profile, Annie Oakley

She and her brother argued about the name spelling? That’s pretty funny. To me the answer was probably “all of the above.” :)

I've been able to find a line for Jacob Moses back to Germany, something I haven't been able to do with Jacob Mosey.
Private Jacob Mosey